Date: Feb 11, 2013 4:19 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
<59abfe03-8386-4d06-8f54-acfbf19a50d0@x15g2000vbj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 11 Feb., 16:40, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 11, 4:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > On 11 Feb., 11:55, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Feb 11, 8:50 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > There exists a natural number m such that d is line number m is false.
> >
> > > Yes so, alas not quite correct if d is assumed to "exist".
> >
> > > If d is assumed to exist, we have
> >
> > > 1) We cannot *find* a natural number m such that d is the m-th line of
> > > the list.

> >
> > According to you
> >
> >    if L is a potentially infinite list, and d is
> >    the potentially infinite diagonal
> >
> >    if for every natural number n, d is not the nth
> >    line of L  then
> >
> >    *There does not exist* a natural number m such that
> >    d is the mth line of L
> >
> > Do you wish to withdraw this claim?

>
> No. This claim is obviously correct.
>
> Only *if the complete existence of the not completely existing
> diagonal d is assumed*, it would be necessary to have it in the list
> and (since every line of the list contains everything that is
> contained by its predecessors) to have it in a line of the list. But
> obviously a potentially infinite diagonal does not exist completely
> (as the potentially infinite list does not exist completely).
>
> So why should anything be withdrawn?


The notion of potential infiniteness should be withdrawn as it is
incompatible with the notion of "set".
One cannot have a set whose membership is only potentially determined.

In all standard set theories there is a set which contains {} as a
member and which for each of its members, m, also contains (m union {m}).

Since this is apparently not the case in WMytheology , then no set
theory in WMytheology is compatible with standard mathematics , and thus
WMytheology irreleveant to standard mathematics.
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